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Question 3 [15 marks] Consider an industry in which there are two firms, a manufacturer and a retailer. The manufacturer moves first, choosing a wholesale price pw for its product. The (monopolistic) retailer observes pw and then decides what quantity q to buy from the manufacturer and then resell to the public. If the retailer sells q units of output then the retail price is pr = A-q where A> 0. Assume for simplicity that manufacturing costs are zero and the retailer's only costs are the payments to the manufacturer. Hence, if the wholesale price is pw and the retailer chooses to buy and then sell q units, then the profits of the manufacturer and retailer arc, respectively, #M(Pw 9) = Pwq and TR(Pw.q) = (A - g)q - pwq. (a) Find the subgame perfect equilibrium of this game. (b) In the subgame perfect equilibrium what is each firm's profit? (c) Suppose that the two firms merge to become a single firm that maximizes joint profits: TM (Pw.q) + TR(pw.g). What happens to the retail price as a result of the merger? How does the profit of the merged firm compare to the sum of the profits in part (b)?